Technical Field
This disclosure generally relates to data storage, search, retrieval, and communication. More specifically, this disclosure relates to performing multidimensional search and content-associative retrieval on data that has been losslessly reduced using a prime data sieve.
Related Art
The modern information age is marked by the creation, capture, and analysis of enormous amounts of data. New data is generated from diverse sources, examples of which include purchase transaction records, corporate and government records and communications, email, social media posts, digital pictures and videos, machine logs, signals from embedded devices, digital sensors, cellular phone global positioning satellites, space satellites, scientific computing, and the grand challenge sciences. Data is generated in diverse formats, and much of it is unstructured and unsuited for entry into traditional databases. Businesses, governments, and individuals generate data at an unprecedented rate and struggle to store, analyze, and communicate this data. Tens of billions of dollars are spent annually on purchases of storage systems to hold the accumulating data. Similarly large amounts are spent on computer systems to process the data.
In most modern computer and storage systems, data is accommodated and deployed across multiple tiers of storage, organized as a storage hierarchy. The data that is needed to be accessed often and quickly is placed in the fastest albeit most expensive tier, while the bulk of the data (including copies for backup) is preferably stored in the densest and cheapest storage medium. The fastest and most expensive tier of data storage is the computer system's volatile random access memory or RAM, residing in close proximity to the microprocessor core, and offering the lowest latency and the highest bandwidth for random access of data. Progressively denser and cheaper but slower tiers (with progressively higher latency and lower bandwidth of random access) include non-volatile solid state memory or flash storage, hard disk drives (HDDs), and finally tape drives.
In order to more effectively store and process the growing data, the computer industry continues to make improvements to the density and speed of the data storage medium and to the processing power of computers. However, the increase in the volume of data far outstrips the improvement in capacity and density of the computing and data storage systems. Statistics from the data storage industry in 2014 reveal that new data created and captured in the past couple of years comprises a majority of the data ever captured in the world. The amount of data created in the world to date is estimated to exceed multiple zettabytes (a zettabyte is 1021 bytes). The massive increase in the data places great demands on data storage, computing, and communication systems that must store, process, and communicate this data reliably. This motivates the increased use of lossless data reduction or compression techniques to compact the data so that it can be stored at reduced cost, and likewise processed and communicated efficiently.
A variety of lossless data reduction or compression techniques have emerged and evolved over the years. These techniques examine the data to look for some form of redundancy in the data and exploit that redundancy to realize a reduction of the data footprint without any loss of information. For a given technique that looks to exploit a specific form of redundancy in the data, the degree of data reduction achieved depends upon how frequently that specific form of redundancy is found in the data. It is desirable that a data reduction technique be able to flexibly discover and exploit any available redundancy in the data. Since data originates from a wide variety of sources and environments and in a variety of formats, there is great interest in the development and adoption of universal lossless data reduction techniques to handle this diverse data. A universal data reduction technique is one which requires no prior knowledge of the input data other than the alphabet; hence, it can be applied generally to any and all data without needing to know beforehand the structure and statistical distribution characteristics of the data.
Goodness metrics that can be used to compare different implementations of data compression techniques include the degree of data reduction achieved on the target datasets, the efficiency with which the compression or reduction is achieved, and the efficiency with which the data is decompressed and retrieved for further use. The efficiency metrics assess the performance and cost-effectiveness of the solution. Performance metrics include the throughput or ingest rate at which new data can be consumed and reduced, the latency or time required to reduce the input data, the throughput or rate at which the data can be decompressed and retrieved, and the latency or time required to decompress and retrieve the data. Cost metrics include the cost of any dedicated hardware components required, such as the microprocessor cores or the microprocessor utilization (central processing unit utilization), the amount of dedicated scratch memory and memory bandwidth, as well as the number of accesses and bandwidth required from the various tiers of storage that hold the data. Note that reducing the footprint of the data while simultaneously providing efficient and speedy compression as well as decompression and retrieval has the benefit not only of reducing the overall cost to store and communicate the data but also of efficiently enabling subsequent processing of the data.
Many of the universal data compression techniques currently being used in the industry derive from the Lempel-Ziv compression method developed in 1977 by Abraham Lempel and Jacob Ziv—see e.g., Jacob Ziv and Abraham Lempel, “A Universal Algorithm for Sequential Data Compression,” IEEE transactions on information theory, Vol. IT-23, No. 3, May 1977. This method became the basis for enabling efficient data transmission via the Internet. The Lempel-Ziv methods (named LZ77, LZ78 and their variants) reduce the data footprint by replacing repeated occurrences of a string with a reference to a previous occurrence seen within a sliding window of a sequentially presented input data stream. On consuming a fresh string from a given block of data from the input data stream, these techniques search through all strings previously seen within the current and previous blocks up to the length of the window. If the fresh string is a duplicate, it is replaced by a backward reference to the original string. If the number of bytes eliminated by the duplicate string is larger than the number of bytes required for the backward reference, a reduction of the data has been achieved. To search through all strings seen in the window, and to provide maximal string matching, implementations of these techniques employ a variety of schemes, including iterative scanning and building a temporary bookkeeping structure that contains a dictionary of all the strings seen in the window. Upon consuming new bytes of input to assemble a fresh string, these techniques either scan through all the bytes in the existing window, or make references to the dictionary of strings (followed by some computation) to decide whether a duplicate has been found and to replace it with a backward reference (or, alternatively, to decide whether an addition needs to be made to the dictionary).
The Lempel-Ziv compression method is often accompanied by a second optimization applied to the data, in which source symbols are dynamically re-encoded based upon their frequency or probability of occurrence in the data block being compressed, often employing a variable-width encoding scheme so that shorter length codes are used for the more frequent symbols, thus leading to a reduction of the data. For example, see David A. Huffman, “A Method for the Construction of Minimum-Redundancy Codes,” Proceedings of the IRE—Institute of Radio Engineers, September 1952, pp. 1098-1101. This technique is referred to as Huffman re-encoding, and typically needs a first pass through the data to compute the frequencies and a second pass to actually encode the data. Several variations along this theme are also in use.
One example that uses these techniques is a scheme known as “Deflate” which combines the Lempel-Ziv LZ77 compression method with Huffman re-encoding. Deflate provides a compressed stream data format specification that specifies a method for representing a sequence of bytes as a (usually shorter) sequence of bits, and a method for packing the latter bit sequences into bytes. The Deflate scheme was originally designed by Phillip W. Katz of PKWARE, Inc. for the PKZIP archiving utility. See e.g., “String searcher, and compressor using same,” Phillip W. Katz, U.S. Pat. No. 5,051,745, Sep. 24, 1991. U.S. Pat. No. 5,051,745 describes a method for searching a vector of symbols (the window) for a predetermined target string (the input string). The solution employs a pointer array with a pointer to each of the symbols in the window, and uses a method of hashing to filter the possible locations in the window that are required to be searched for an identical copy of the input string. This is followed by scanning and string matching at those locations.
The Deflate scheme is implemented in the zlib library for data compression. Zlib is a software library that is a key component of several software platforms such as Linux, Mac OS X, iOS, and a variety of gaming consoles. The zlib library provides Deflate compression and decompression code for use by zip (file archiving), gzip (single file compression), png (Portable Network Graphics format for losslessly compressed images), and many other applications. Zlib is now widely used for data transmission and storage. Most HTTP transactions by servers and browsers compress and decompress the data using zlib. Similar implementations are increasingly being used by data storage systems.
A paper entitled “High Performance ZLIB Compression on Intel® Architecture Processors,” that was published by Intel Corp. in April 2014 characterizes the compression and performance of an optimized version of the zlib library running on a contemporary Intel processor (Core I7 4770 processor, 3.4 GHz, 8 MB cache) and operating upon the Calgary corpus of data. The Deflate format used in zlib sets the minimum string length for matching to be 3 characters, the maximum length of the match to be 256 characters, and the size of the window to be 32 kilobytes. The implementation provides controls for 9 levels of optimization, with level 9 providing the highest compression but using the most computation and performing the most exhaustive matching of strings, and level 1 being the fastest level and employing greedy string matching. The paper reports a compression ratio of 51% using the zlib level 1 (fastest level) using a single-threaded processor and spending an average of 17.66 clocks/byte of input data. At a clock frequency of 3.4 GHz, this implies an ingest rate of 192 MB/sec while using up a single microprocessor core. The report also describes how the performance rapidly drops to an ingest rate of 38 MB/sec (average of 88.1 clocks/byte) using optimization level 6 for a modest gain in compression, and to an ingest rate of 16 MB/sec (average of 209.5 clocks/byte) using optimization level 9.
Existing data compression solutions typically operate at ingest rates ranging from 10 MB/sec to 200 MB/sec using a single processor core on contemporary microprocessors. To further boost the ingest rate, multiple cores are employed, or the window size is reduced. Even further improvements to the ingest rate are achieved using custom hardware accelerators, albeit at increased cost.
Existing data compression methods described above are effective at exploiting fine-grained redundancy at the level of short strings and symbols in a local window typically the size of a single message or file or perhaps a few files. These methods have serious limitations and drawbacks when they are used in applications that operate on large or extremely large datasets and that require high rates of data ingestion and data retrieval.
One important limitation is that practical implementations of these methods can exploit redundancy efficiently only within a local window. While these implementations can accept arbitrarily long input streams of data, efficiency dictates that a limit be placed on the size of the window across which fine-grained redundancy is to be discovered. These methods are highly compute-intensive and need frequent and speedy access to all the data in the window. String matching and lookups of the various bookkeeping structures are triggered upon consuming each fresh byte (or few bytes) of input data that creates a fresh input string. In order to achieve desired ingest rates, the window and associated machinery for string matching must reside mostly in the processor cache subsystem, which in practice places a constraint on the window size.
For example, to achieve an ingest rate of 200 MB/sec on a single processor core, the available time budget on average per ingested byte (inclusive of all data accesses and compute) is 5 ns., which means 17 clocks using a contemporary processor with operating frequency of 3.4 GHz. This budget accommodates accesses to on-chip caches (which take a handful of cycles) followed by some string matching. Current processors have on-chip caches of several megabytes of capacity. An access to main memory takes over 200 cycles (˜70 ns.), so larger windows residing mostly in memory will further slow the ingest rate. Also, as the window size increases, and the distance to a duplicate string increases, so does the cost to specify the length of backward references, thus encouraging only longer strings to be searched across the wider scope for duplication.
On most contemporary data storage systems, the footprint of the data stored across the various tiers of the storage hierarchy is several orders of magnitude larger than the memory capacity in the system. For example, while a system could provide hundreds of gigabytes of memory, the data footprint of the active data residing in flash storage could be in the tens of terabytes, and the total data in the storage system could be in the range of hundreds of terabytes to multiple petabytes. Also, the achievable throughput of data accesses to subsequent tiers of storage drops by an order of magnitude or more for each successive tier. When the sliding window gets so large that it can no longer fit in memory, these techniques get throttled by the significantly lower bandwidth and higher latency of random IO (Input or Output operations) access to the next levels of data storage.
For example, consider a file or a page of 4 kilobytes of incoming data that can be assembled from existing data by making references to, say, 100 strings of average length of 40 bytes that already exist in the data and are spread across a 256 terabyte footprint. Each reference would cost 6 bytes to specify its address and 1 byte for string length while promising to save 40 bytes. Although the page described in this example can be compressed by more than fivefold, the ingest rate for this page would be limited by the 100 or more IO accesses to the storage system needed to fetch and verify the 100 duplicate strings (even if one could perfectly and cheaply predict where these strings reside). A storage system that offers 250,000 random IO accesses/sec (which means bandwidth of 1 GB/sec of random accesses to pages of 4 KB) could compress only 2,500 such pages of 4 KB size per second for an ingest rate of a mere 10 MB/sec while using up all the bandwidth of the storage system, rendering it unavailable as a storage system.
Implementations of conventional compression methods with large window sizes of the order of terabytes or petabytes will be starved by the reduced bandwidth of data access to the storage system, and would be unacceptably slow. Hence, practical implementations of these techniques efficiently discover and exploit redundancy only if it exists locally, on window sizes that fit in the processor cache or system memory. If redundant data is separated either spatially or temporally from incoming data by multiple terabytes, petabytes, or exabytes, these implementations will be unable to discover the redundancy at acceptable speeds, being limited by storage access bandwidth.
Another limitation of conventional methods is that they are not suited for random access of data. Blocks of data spanning the entire window that was compressed need to be decompressed before any chunk within any block can be accessed. This places a practical limit on the size of the window. Additionally, operations (e.g., a search operation) that are traditionally performed on uncompressed data cannot be efficiently performed on the compressed data.
Yet another limitation of conventional methods (and, in particular, Lempel-Ziv based methods) is that they search for redundancy only along one dimension—that of replacing identical strings by backward references. A limitation of the Huffman re-encoding scheme is that it needs two passes through the data, to calculate frequencies and then re-encode. This becomes slow on larger blocks.
Data compression methods that detect long duplicate strings across a global store of data often use a combination of digital fingerprinting and hashing schemes. This compression process is referred to as data deduplication. The most basic technique of data deduplication breaks up files into fixed-sized blocks and looks for duplicate blocks across the data repository. If a copy of a file is created, each block in the first file will have a duplicate in the second file and the duplicate can be replaced with a reference to the original block. To speed up matching of potentially duplicate blocks, a method of hashing is employed. A hash function is a function that converts a string into a numeric value, called its hash value. If two strings are equal, their hash values are also equal. Hash functions map multiple strings to a given hash value, whereby long strings can be reduced to a hash value of much shorter length. Matching of the hash values will be much faster than matching of two long strings; hence, matching of the hash values is done first, to filter possible strings that might be duplicates. If the hash value of the input string or block matches a hash value of strings or blocks that exist in the repository, the input string can then be compared with each string in the repository that has the same hash value to confirm the existence of the duplicate.
Breaking up a file into fixed-sized blocks is simple and convenient, and fixed-sized blocks are highly desirable in a high-performance storage system. However, this technique has limitations in the amount of redundancy it can uncover, which means that these techniques have low levels of compression. For example, if a copy of a first file is made to create a second file, and if even a single byte of data is inserted into the second file, the alignment of all downstream blocks will change, the hash value of each new block will be computed afresh, and the data deduplication method will no longer find all the duplicates.
To address this limitation in data deduplication methods, the industry has adopted the use of fingerprinting to synchronize and align data streams at locations of matching content. This latter scheme leads to variable-sized blocks based on the fingerprints. Michael Rabin showed how randomly chosen irreducible polynomials can be used to fingerprint a bit-string—see e.g., Michael O. Rabin, “Fingerprinting by Random Polynomials,” Center for Research in Computing Technology, Harvard University, TR-15-81, 1981. In this scheme, a randomly chosen prime number p is used to fingerprint a long character-string by computing the residue of that string viewed as a large integer modulo p. This scheme requires performing integer arithmetic on k-bit integers, where k=log2(p). Alternatively, a random irreducible prime polynomial of order k can be used, and the fingerprint is then the polynomial representation of the data modulo the prime polynomial.
This method of fingerprinting is used in data deduplication systems to identify suitable locations at which to establish chunk boundaries, so that the system can look for duplicates of these chunks in a global repository. Chunk boundaries can be set upon finding fingerprints of specific values. As an example of such usage, a fingerprint can be calculated for each and every 48-byte string in the input data (starting at the first byte of the input and then at every successive byte thereafter), by employing a polynomial of order 32 or lower. One can then examine the lower 13 bits of the 32-bit fingerprint, and set a breakpoint whenever the value of those 13 bits is a pre-specified value (e.g., the value 1). For random data, the likelihood of the 13 bits having that particular value would be 1 in 213, so that such a breakpoint is likely to be encountered approximately once every 8 KB, leading to variable-sized chunks of average size 8 KB. The breakpoints or chunk boundaries will effectively be aligned to fingerprints that depend upon the content of the data. When no fingerprint is found for a long stretch, a breakpoint can be forced at some pre-specified threshold, so that the system is certain to create chunks that are shorter than a pre-specified size for the repository. See e.g., Athicha Muthitacharoen, Benjie Chen, and David Mazières, “A Low-bandwidth Network File System,” SOSP '01, Proceedings of the eighteenth ACM symposium on Operating Systems Principles, Oct. 21, 2001, pp. 174-187.
The Rabin-Karp string matching technique developed by Michael Rabin and Richard Karp provided further improvements to the efficiency of fingerprinting and string matching (see e.g., Michael O. Rabin and R. Karp, “Efficient Randomized Pattern-Matching Algorithms,” IBM Jour. of Res. and Dev., vol. 31, 1987, pp. 249-260). Note that a fingerprinting method that examines an m byte substring for its fingerprint can evaluate the fingerprinting polynomial function in O(m) time. Since this method would need to be applied on the substring starting at every byte of the, say, n byte input stream, the total effort required to perform fingerprinting on the entire data stream would be O(n×m). Rabin-Karp identified a hash function referred to as a Rolling Hash on which it is possible to compute the hash value of the next substring from the previous one by doing only a constant number of operations, independently of the length of the substring. Hence, after shifting one byte to the right, the computation of the fingerprint on the new m byte string can be done incrementally. This reduces the effort to compute the fingerprint to O(1), and the total effort for fingerprinting the entire data stream to O(n), linear with the size of the data. This greatly speeds up computation and identification of the fingerprints.
Typical data access and computational requirements for the above-described data deduplication methods can be described as follows. For a given input, once fingerprinting is completed to create a chunk, and after the hash value for the chunk is computed, these methods first need one set of accesses to memory and subsequent tiers of storage to search and look up the global hash table that keeps the hash values of all chunks in the repository. This would typically need a first IO access to storage. Upon a match in the hash table, this is followed by a second set of storage IOs (typically one, but could be more than one depending upon how many chunks with the same hash value exist in the repository) to fetch the actual data chunks bearing the same hash value. Lastly, byte-by-byte matching is performed to compare the input chunk to the fetched potentially matching chunks to confirm and identify the duplicate. This is followed by a third storage IO access (to the metadata space) for replacing the new duplicate block with a reference to the original. If there is no match in the global hash table (or if no duplicate is found), the system needs one IO to enter the new block into the repository and another IO to update the global hash table to enter in the new hash value. Thus, for large datasets (where the metadata and global hash table do not fit in memory, and hence need a storage IO to access them) such systems could need an average of three IOs per input chunk. Further improvements are possible by employing a variety of filters so that misses in the global hash table can often be detected without requiring the first storage IO to access the global hash table, thus reducing the number of IOs needed to process some of the chunks down to two.
A storage system that offers 250,000 random IO accesses/sec (which means bandwidth of 1 GB/sec of random accesses to pages of 4 KB) could ingest and deduplicate about 83,333 (250,000 divided by 3 IOs per input chunk) input chunks of average size 4 KB per second, enabling an ingest rate of 333 MB/sec while using up all the bandwidth of the storage system. If only half of the bandwidth of the storage system is used (so that the other half is available for accesses to the stored data), such a deduplication system could still deliver ingest rates of 166 MB/sec. These ingest rates (which are limited by I/O bandwidth) are achievable provided that sufficient processing power is available in the system. Thus, given sufficient processing power, data deduplication systems are able to find large duplicates of data across the global scope of the data with an economy of IOs and deliver data reduction at ingest rates in the hundreds of megabytes per second on contemporary storage systems.
Based on the above description, it should be clear that, while these deduplication methods are effective at finding duplicates of long strings across a global scope, they are effective mainly at finding large duplicates. If there are variations or modifications to the data at a finer grain, the available redundancy will not be found using this method. This greatly reduces the breadth of datasets across which these methods are useful. These methods have found use in certain data storage systems and applications, e.g., regular backup of data, where the new data being backed up has only a few files modified and the rest are all duplicates of the files that were saved in the previous backup. Likewise, data deduplication based systems are often deployed in environments where multiple exact copies of the data or code are made, such as in virtualized environments in datacenters. However, as data evolves and is modified more generally or at a finer grain, data deduplication based techniques lose their effectiveness.
Some approaches (usually employed in data backup applications) do not perform the actual byte-by-byte comparison between the input data and the string whose hash value matches that of the input. Such solutions rely on the low probability of a collision using strong hash functions like the SHA-1. However, due to the finite non-zero probability of a collision (where multiple different strings could map to the same hash value), such methods cannot be considered to provide lossless data reduction, and would not, therefore, meet the high data-integrity requirements of primary storage and communication.
Some approaches combine multiple existing data compression techniques. Typically, in such a setup, the global data deduplication methods are applied to the data first. Subsequently, on the deduplicated dataset, and employing a small window, the Lempel-Ziv string compression methods combined with Huffman re-encoding are applied to achieve further data reduction.
However, in spite of employing all hitherto-known techniques, there continues to be a gap of several orders of magnitude between the needs of the growing and accumulating data and what the world economy can affordably accommodate using the best available modern storage systems. Given the extraordinary requirements of storage capacity demanded by the growing data, there continues to be a need for improved ways to further reduce the footprint of the data. There continues to be a need to develop methods that address the limitations of existing techniques, or that exploit available redundancy in the data along dimensions that have not been addressed by existing techniques. At the same time, it continues to be important to be able to efficiently access and retrieve the data at an acceptable speed and at an acceptable cost of processing.
In summary, there continues to be a long-felt need for lossless data reduction solutions that can exploit redundancy across large and extremely large datasets and provide high rates of data ingestion and data retrieval.